I know you have already done the firmware update, but it would be worthwhile using the Slackbuilds from
http://slackbuilds.org/result/?search=b43&sv=13.37 to build and install the b43-firmware. This will give confidence that everything is done in the way that Slackware 13.37 expects.
Does your wireless card appear in the listing from 'ifconfig -a'? I would expect an interface wlan0.
If you can see wlan0, what is the output from 'iwconfig wlan0'?
I believe you are close with this, with some final configuration to go. I would not worry about other devices just yet.